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Boundedness and compactness of positive integral operators on cones of homogeneous groups

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Necessary and sufficient conditions on a weight function v guaranteeing the boundedness/compactness of integral operators with positive kernels defined on cones of homogeneous groups from Lp to L q v are established, where \(1< p,q < \infty\) or \(0 < q \leq 1< p < \infty\). Behavior of singular numbers for these operators is also studied.

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Authors and Affiliations

  1. Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan

    Usman Ashraf & Muhammad Asif

  2. Georgian Academy of Sciences, A. Razmadze Mathematical Institute, 1, M. Aleksidze St, 0193, Tbilisi, Georgia

    Alexander Meskhi

Authors
  1. Usman Ashraf
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  2. Muhammad Asif
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  3. Alexander Meskhi
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Correspondence to Alexander Meskhi.

Additional information

The work was partially supported by the INTAS grant No. 05-1000008-8157 and the Georgian National Foundation Grant No. GNSF/ST06/3-010.

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Ashraf, U., Asif, M. & Meskhi, A. Boundedness and compactness of positive integral operators on cones of homogeneous groups. Positivity 13, 497–518 (2009). https://doi.org/10.1007/s11117-008-2217-8

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